Bcom Bachelor of Commerce Business Statistics 2 — Questions and Answers
Question 1: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
- 68% (Correct answer)
- 95%
- 99.7%
- 50%
Correct answer: 68%
The empirical rule states that about 68% of observations in a normal distribution fall within ±1 standard deviation of the mean.
Question 2: What is 'simple linear regression' used for?
- Modeling the relationship between one independent variable and one dependent variable (Correct answer)
- Comparing means across multiple groups
- Testing whether two variables are independent
- Measuring correlation between ranked variables
Correct answer: Modeling the relationship between one independent variable and one dependent variable
Simple linear regression estimates how changes in one predictor variable (X) are associated with changes in an outcome variable (Y) using the equation Y = a + bX.
Question 3: What does a correlation coefficient of +1 indicate?
- A perfect positive linear relationship between two variables (Correct answer)
- A weak positive association
- No relationship between variables
- A perfect negative relationship
Correct answer: A perfect positive linear relationship between two variables
A correlation of +1 means the two variables move together in perfect lockstep—when one increases, the other increases by a proportional amount.
Question 4: What is a 'Type I error' in hypothesis testing?
- Rejecting a true null hypothesis (false positive) (Correct answer)
- Failing to reject a false null hypothesis
- Using the wrong statistical test
- Collecting an insufficient sample
Correct answer: Rejecting a true null hypothesis (false positive)
A Type I error (false positive) occurs when a researcher incorrectly rejects the null hypothesis when it is actually true.
Question 5: In a frequency distribution, the 'class interval' refers to:
- The width or size of each group in the distribution (Correct answer)
- The number of observations in each class
- The midpoint of each class
- The total number of classes
Correct answer: The width or size of each group in the distribution
The class interval (or class width) is the range of values covered by each group in a frequency distribution, calculated as upper boundary minus lower boundary.
Question 6: What is 'stratified random sampling'?
- Dividing the population into subgroups and randomly sampling from each subgroup (Correct answer)
- Randomly selecting every nth item from a list
- Choosing the most convenient available subjects
- Sampling entire naturally occurring groups
Correct answer: Dividing the population into subgroups and randomly sampling from each subgroup
Stratified sampling ensures representation from each population subgroup (stratum) by randomly selecting samples within each stratum.
Bcom Bachelor of Commerce Business Statistics 2
In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?